Parametric Power Multiplication

ABSTRACT

In various embodiments, power multipliers and associated methods are provided that employ parametric excitation. In one embodiment, a ring power multiplier is provided that has a ring. A parametric reactance is associated with the ring that negates at least a portion of a physical resistance of the ring.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of co-pending U.S. Utilitypatent application Ser. No. 11/069,476 entitled, “ELECTRICAL POWERMULTIPLICATION,” filed on Mar. 1, 2005, which is continuation-in-part ofU.S. Utility patent application Ser. No. 11/062,035 entitled “ELECTRICALPOWER MULTIPLICATION” filed on Feb. 18, 2005, now abandoned, both ofwhich are incorporated herein by reference in their entirety. Thisapplication is also a continuation-in-part of co-pending U.S. Utilitypatent application Ser. No. 11/069,682 entitled, “USE OF ELECTRICALPOWER MULTIPLICATION FOR POWER SMOOTHING IN POWER DISTRIBUTION,” filedon Mar. 1, 2005, which is continuation-in-part of U.S. Utility patentapplication Ser. No. 11/062,179 entitled “USE OF ELECTRICAL POWERMULTIPLICATION FOR POWER SMOOTHING IN POWER DISTRIBUTION” filed on Feb.18, 2005, now abandoned, both of which are incorporated herein byreference in their entirety.

BACKGROUND

Power multiplication may be desirable for many applications that requiresignificant power resources that cannot be economically or physicallyprovided given the current state of power technology. For example, somehave attempted to use conventional mechanical flywheel and capacitivestorage arrangements for energy storage and power multiplication.However, such approaches are often inadequate due to the decay inamplitude and/or frequency of power output as stored energy is extractedor released.

Power multiplication may also be achieved electrically using anelectromagnetic path configuration for accumulating electrical energyand stepping up or magnifying real AC power. Such technology has beentaught by Tischer, F. J., Resonance Properties of Ring Circuits, IEEETransactions on Microwave Theory and Techniques, Vol. MTT-5, 1957, pp.51-56. The power multiplier suggested by Tischer makes it possible toobtain practical power multiplication of 10 to 500 times the outputpower level of a given generator. The power multiplication is obtainedwithout appreciable decay in either amplitude or frequency.

However, the power multiplier suggested by Tischer operates atrelatively short wavelengths where the physical circumference of thedevice is on the order of an integral number of free space wavelengthsgiven that the electrical length of the electromagnetic path suggestedby Tischer equals an integer multiple of the wavelength of a travelingwave multiplied therein. At such short wavelengths, the physical size ofthe electromagnetic path is such that it can be practically constructed.However, power multiplication using an approach suggested by Tischer isnot practical at lower power frequencies such as 60 Hertz withrelatively long wavelengths as the size of the electromagnetic pathwould be on the order of several hundred miles. In addition, the maximumpower that can be stored in the power multiplier suggested by Tischer islimited by the resistance of the waveguide.

In current electrical distribution systems such as the North Americanpower grid it is often the case that Utilities experience severemismatches between peak and average load demands. This can result inbrown outs and blackouts in the system. Also, the North American powergrid is being stretched to capacity. Consequently, it can be the casethat brown outs and black outs may start chain reactions in the powergrid that results in loss of reliable power.

In addition, another problem that energy markets face is thatintervening load points such as cities often separate power generationstations from remote electrical loads. During heavy load times, thedemand throughput cannot be conveyed from the power generation stationsto the remote loads around the intermediate cities.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the invention can be better understood with reference tothe following drawings. The components in the drawings are notnecessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present invention. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 is a drawing of a power multiplier according to the prior art;

FIG. 2 is a drawing of a directional coupler of the power multiplier ofFIG. 1;

FIG. 3 is a drawing of an impractical power multiplier with respect to ageographical map illustrating a problem of practicing powermultiplication using a power multiplier illustrated in FIG. 1 at powerfrequencies of relatively small wavelengths;

FIG. 4A is a block diagram of power transmission line from a powergenerator to an electrical load;

FIG. 4B is a schematic of an equivalent impedance per length oftransmission line of FIG. 4A;

FIG. 5 is a drawing of alternative transmission lines that might beemployed as the power transmission line of FIG. 4A and that have anequivalent impedance that can be modeled by the schematic of FIG. 4B;

FIG. 6A is a schematic of a T-network employed in a power multiplieraccording to an embodiment of the present invention;

FIG. 6B is a schematic of a π-network employed in a power multiplieraccording to an embodiment of the present invention;

FIG. 7A is a schematic of an embodiment of the T-network of FIG. 6A;

FIG. 7B is a schematic of an embodiment of the π-network of FIG. 6B;

FIG. 8 is a schematic of a power multiplying network according to anembodiment of the present invention;

FIG. 9 is a schematic of a phase shifter employed in the powermultiplier of FIG. 8 according to an embodiment of the presentinvention;

FIG. 10 is a schematic of a directional coupler employed in the powermultiplier of FIG. 8 according to an embodiment of the presentinvention;

FIG. 11 is a schematic of a second power multiplier according toembodiment of the present invention;

FIG. 12 is a schematic diagram of a power multiplier coupled to a powerdistribution network according to an embodiment of the presentinvention;

FIG. 13 is a schematic diagram of multiple power multiplier coupled to apower distribution network according to an embodiment of the presentinvention;

FIG. 14 is schematic of a power multiplying network according to anembodiment of the present invention; and

FIG. 15 is a schematic of a power multiplying network according to anembodiment of the present invention.

DETAILED DESCRIPTION

With reference to FIG. 1, shown is a power multiplier 100 according tothe prior art. The power multiplier 100 includes a power multiplyingwaveguide 103 and a launching waveguide 106. Both the power multiplyingwaveguide 103 and the launching waveguide 106 are conventionaltransmission lines such as hollow pipes, coaxial cables, parallel wiretransmission lines. The launching waveguide 106 is coupled to the powermultiplying waveguide 103 using a directional coupler 109. Anelectromagnetic signal generator 113 is coupled to the launchingwaveguide 106 and generates an exciting traveling wave 116 that islaunched into the launching waveguide 106. The directional coupler 109includes two slits 119 that are spaced apart by distance D. The distanceD is approximately equal to ¼ of wavelength of the exciting travelingwave 116. Thus, the electromagnetic signal generator 113 generates theexciting traveling wave 116 at a predefined frequency having awavelength λ_(W) that is approximately four times the electricaldistance D/λ_(W). The launching waveguide 106 terminates in a matchedload 123. The total length of the power multiplying waveguide 103 is aninteger multiple of the wavelength λ_(W) of the exciting traveling wave116. In the case that the power multiplying waveguide 103 is a closedcircle or closed ring as shown, the total length of the powermultiplying waveguide is equal to its circumference.

To operate the power multiplier 100, the electromagnetic signalgenerator 113 generates the exciting traveling wave 116 that is launchedin the launching waveguide 106. When the exciting traveling wave 116reaches the directional coupler 109, a portion of the exciting travelingwave 116 is coupled into the power multiplying waveguide 103, therebycreating a traveling wave 126 that propagates along the powermultiplying waveguide 103. The directional coupler 109 couples theportion of the exciting traveling wave 116 into the power multiplyingwaveguide 103 in such a manner that the traveling wave 116 travels in asingle direction around the power multiplying waveguide 103.Specifically, since the distance D between the slits 119 isapproximately equal to ¼ of the wavelength λ_(W) of the excitingtraveling wave 116, all energy coupled into the power multiplyingwaveguide 103 propagates in a single direction as will be furtherdescribed with reference to later figures.

In addition, since the length of the power multiplying waveguide 103 isan integer multiple of the wavelength λ_(W) of the exciting travelingwave 116, the traveling wave 126 is spatially synchronized with theexciting traveling wave 116. Under these conditions, the portion of theexciting traveling wave 116 that is continually coupled into the powermultiplying waveguide 103 reinforces or is added to the traveling wave126. Consequently, the power of the traveling wave 126 may become quitelarge in magnitude. That is to say, the Poynting's vector power flow,½Re{E×H*} is pumped up within the power multiplying waveguide, which isa linear, passive, distributed energy storage structure. The averageenergy of the traveling wave 126 is “distributed” in that it is evenlydistributed throughout the entire length of the power multiplyingwaveguide 103.

Once begun, the buildup of the power of the traveling wave 126 withinthe power multiplying waveguide 103 will continue until the lossesaround the power multiplying waveguide 103 plus the loss in the matchedload 123 that terminates the launching waveguide 106 is equal to thepower generated by the electromagnetic signal generator 113. The powermagnification M and optimum coupling C_(Opt) may be calculated asfollows: $\begin{matrix}{{M = \frac{1}{\left( {1 - A^{2}} \right)}},\quad{and}} \\{{C_{Opt} = {1 - A^{2}}},}\end{matrix}$where A is the field propagation decay for a single traversal of thepower multiplying waveguide 103. The quantity of C_(Opt) is that valueof coupling for which the magnification is maximized.

The directional coupler has the property that energy leaking from thepower multiplying waveguide 103 back into the launching waveguide 106 isreduced in magnitude. Also, energy leaking back into the launchingwaveguide 106 propagates only in a single direction towards the matchedload 123 and, since such energy is of the correct phase, it cancels outthe power propagating from the electromagnetic signal generator 113 tothe matched load 123. Consequently, when the exciting traveling wave 126and the traveling wave 126 are in phase, the matched load 123 dissipateslittle or no power. Convenient nomograms for the engineering design oflossy power multipliers operating at ultra-high frequencies aredescribed in Tomiyasu, K., “Attenuation in a Resonant Ring Circuit,”IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-8, 1960,pp. 253-254.

Referring next to FIG. 2, shown is a drawing of a portion of the powermultiplying waveguide 103 and a portion of the launching waveguide 106.Also shown is the directional coupler 109. The drawing of FIG. 2 isprovided to further explain the function of the directional coupler 109.To explain the operation of the directional coupler 109, the excitingtraveling wave 116 is launched into the launching waveguide 106 andapproaches the first slit 119 a. A portion of the exciting travelingwave 116 enters the power multiplying waveguide 103 through the firstslit 119 a propagates in both directions within the power multiplyingwaveguide 103 as wave portion W₁ and wave portion W₂. The portion of theexciting traveling wave 116 that does not pass through the first slit119 a proceeds along the launching waveguide 106 until it reaches thesecond slit 119 b. At this point, a second portion of the excitingtraveling wave 116 enters the power multiplying waveguide 103 throughthe second slit 109 b and propagates in both directions in the powermultiplying waveguide 103 as wave portion W₃ and wave portion W₄. If thedistance D between the slits is equal to ¼ of the wavelength λ_(W) ofthe exciting traveling wave 116 as shown, then the wave portion W₃cancels out the wave portion W₁. Also, the wave portion W₂ reinforcesthe wave portion W₄, thereby resulting in the traveling wave 126. As aconsequence of the cancellation of wave portions W₁ and W₃, and thereinforcement of wave portions W₂ and W₄, the traveling wave 126proceeds in a single direction around the power multiplying waveguide126. Given that the exciting traveling wave 116 and the traveling wave126 are in phase or are spatially synchronized, the portion of theexciting traveling wave 116 that is coupled into the power multiplyingwaveguide 103 is continually added to the traveling wave 126, therebymultiplying the power of the traveling wave 126. The power of thetraveling wave 126 is real power. This is to say that there is noreactive component.

Referring next to FIG. 3, shown is a drawing of a map of the UnitedStates 133 that illustrates the problem that prevents the operation ofpower multipliers 100 at low frequencies such as power frequencies.Assume, for example, that the frequency of operation is 60 Hertz whichrepresents the frequency of the power generation system of the UnitedStates. Assuming that the speed of light is approximately 300,000km/sec, at 60 Hertz, the wavelength of both the exciting traveling wave116 and the traveling wave 126 is calculated as: $\begin{matrix}{\lambda_{w} = \frac{c}{f}} \\{\approx \frac{300\text{,}000\quad{km}\text{/}\sec}{60\quad{Hz}}} \\{\approx {5000\quad{{km}.}}}\end{matrix}$

Thus, the length or circumference of a hypothetical power multiplyingwaveguide 100 a would have to be approximately 5000 Kilometers.Consequently, a corresponding hypothetical transmission line 101employed in the power multiplying waveguide 100 a would be approximately5000 Kilometers in length. Obviously, due to the size involved, thecreation of such a power multiplying waveguide 100 a is not physicallypractical and is cost prohibitive.

Turning then to FIG. 4A, we turn our attention to a discussion of powertransmission lines. In FIG. 4A, a power generator 153 is electricallycoupled to an electrical load 156 by a power transmission line 159. Sucha transmission line 159 may be traditionally employed, for example, todistribute power to homes and businesses as can be appreciated by thosewith ordinary skill in the art.

Referring next to FIG. 4B, shown is an equivalent circuit 163 thatillustrates the equivalent impedance per unit length of the transmissionline 159 (FIG. 4A). Specifically, each unit length of the transmissionline 159 includes series inductance L_(T) and series resistance R_(T).Also, between the conductors of the transmission line 159 are a shuntcapacitance C_(T) and a shunt conductance G_(T). Accordingly, theequivalent impedance per unit length of the transmission line 159 may beexpressed in terms of a series inductance L_(T), a series resistanceR_(T), a shunt capacitance C_(T), and a shunt resistance R_(T).

The equivalent circuit 163 reflects that fact that transmission lines159 direct the propagation of field energy. The field energy propagatingalong a transmission line 159 is stored in the magnetic fields andelectric fields associated with the structure of the transmission line159 itself. On a mode-by-mode basis, one can equate the magnetic fieldenergy stored in a transmission line 159 to the magnetic field energystored in an equivalent distributed inductance. Also, the energy storedin the electric fields of the line can be equated to the energy storedin an equivalent distributed capacitance. Field power losses per unitlength of the transmission line 159 can be equated to the equivalentseries resistive and shunt conductive losses per unit length.

Turning then to FIG. 5, shown are various embodiments of thetransmission line 159 (FIG. 4A) for which the equivalent impedance maybe expressed using the equivalent circuit 163 (FIG. 4B) discussed above.For example, transmission line 159 may comprise, for example, a paralleltransmission line 159 a that includes parallel conductors 166.Alternatively, the transmission line 159 may comprise a coaxialtransmission line 159 b that includes an inner conductor 169 and anouter conductor 173. In yet another alternative, the transmission line159 may comprise an electrical structure 159 c that includes a conductor176 of a predefined geometry situated with respect to a ground plane179. Alternatively, the conductor 176 may be situated with respect to asecond such conductor rather than the ground plane 179. The predefinedgeometry of the conductor 176 may be, for example, a helix or othergeometry. In still another alternative, the transmission line 159 maycomprise an electrical structure 159 d that comprises a single conductor181 in the form a helix or other appropriate shape. In addition thetransmission line 159 may comprise other types of transmission lines andelectrical structures such as, for example, strip lines, fiber opticcables, and so on as can be appreciated by those with ordinary skill inthe art.

Assuming that were actually possible to create the power multiplier 100a at power frequencies such as 60 Hertz, such a power multiplier 100 awould involve the use of transmission wire in one of the configurationsdescribed above. In this respect, the impedance of such a transmissionwire can be calculated and the equivalent impedance in terms of theseries inductance L_(T) (FIG. 4B), the series resistance R_(T) (FIG.4B), the shunt capacitance C_(T) (FIG. 4B), and the shunt conductanceG_(T) (FIG. 4B) can be determined.

With reference to FIGS. 6A and 6B, shown are a T-network 183 and aπ-network 186 that may be employed according to the various embodimentsof the present invention. In this respect, the T-Network 183 includesseries impedance Z₁ and series impedance Z₂. The T-Network 183 alsoincludes parallel impedance Z₃. The characteristic impedance Z₀ of asymmetrical T-network 183 shown may be calculated as follows:Z ₀ =√{square root over (Z₁(Z₁(Z₁+2Z₃))}.

The π-network 186 includes parallel impedances Z_(A) and Z_(B). Theπ-network 186 also includes series or middle impedance Z_(C). Thecharacteristic impedance Z₀ of a symmetrical π-network 186 may becalculated as follows:$Z_{0} = {Z_{A}{\sqrt{\frac{Z_{C}}{\left( {Z_{C} + {2Z_{A}}} \right)}}.}}$

For further discussion of both the T-network 183 and/or the π-network186, reference is made to Terman, F. E., Radio Engineering Handbook,McGraw-Hill, 1943, pp. 172-178, 191-215, which is incorporated herein byreference in its entirety. The T-network 183 and/or the π-network 186may be employed, for example, in the construction of a power multiplieraccording to various embodiments of the present invention as will bediscussed. In particular, the impedance represented by the T-network 183and/or the π-network 186 are forms of the equivalent circuit 163 (FIG.4B).

Referring next to FIGS. 7A and 7B, shown are an example schematic ofboth a T-network 183 a and a π-network 186 a that may be employed invarious embodiments of the present invention. In this respect, theT-network 183 a includes series inductance L that is shown as twoseparate series inductances L/2. In addition, the T-network 183 a alsoincludes a shunt capacitance C. The T-network 183 a includes a seriesloss resistances R and a shunt conductance G that are inherent in theconductors making up the inductances L/2, the capacitance C, and theelectrical wire connecting such components.

The π-network 186 a includes a series inductance L and shuntcapacitances C/2. For multiple π-networks 186 a that are coupledtogether in series, adjacent shunt capacitances C/2 may be addedtogether to become capacitance C. The π-networks 186 a also includes aseries resistance R and a shunt conductance G that are inherent in theconductors making up the inductance L, the capacitances C/2, and theelectrical wire connecting such components. The T-network 183 a andπ-network 186 a illustrate more particular embodiments of the T-networks183 or π-networks 186.

Turning then, to FIG. 8, shown is an example of a power multiplier 200according to an embodiment of the present invention. The powermultiplier 200 includes a power multiplying network 203 and a launchingnetwork 206. The launching network 206 also includes a directionalcoupler 209 that couples the launching network 206 to the powermultiplying network 203. A power source 213 is coupled to the launchingnetwork 206. Also, the launching network 206 is terminated in a matchingload R_(L).

In one embodiment, the power multiplying network 203 is amultiply-connected, velocity inhibiting circuit constructed from anumber of lumped-elements 216. As contemplated herein, the term“network” is defined as an interconnected structure of electricalelements. The terms “multiply-connected” is a mathematical termdescribing the existence of a closed path in a resonator, waveguide, orother electrical structure that cannot be reduced to a point withoutpart of the closed path passing through regions that are external to thegeometrical boundaries of the resonator, waveguide, or other electricalpathway. The power multiplying network 203 is “velocity inhibiting” asthe electrical structure of the power multiplying network 203 results ina reduced velocity of propagation of an electromagnetic wave through thepower multiplying network 203 relative to the speed of anelectromagnetic wave through free space, which is the speed of light.

In addition, the term “lumped” is defined herein as effectivelyconcentrated at a single location. Thus, the terms “lumped-elements”refer to discrete, two-terminal, concentrated electrical elements suchas capacitance, inductances, resistance, and/or conductance. Thus, thelumped-elements as described herein may comprise discrete inductors,capacitors, or resistors. In addition, as contemplated herein,lumped-elements may also comprise diodes, transistors, and othersemi-conductors that may be described, for example, as nonlinearresistors or conductors that have resistance or conductance that iscontrolled by the polarity of applied voltages or currents, etc. Inaddition, lumped-elements may also comprise inherent capacitances,inductances, resistances, or conductances of various electricalstructures such as helices, parallel plates, or other structure as willbe discussed. Similar to the power multiplying network 203, thedirectional coupler 209 is also constructed using lumped-elements.

The power multiplying network 203 is a velocity inhibiting circuit thatresults in a slower velocity of propagation of an electrical disturbancesuch as a traveling wave. In this respect, the power multiplying network203 has an electrical length that is equal to an integer multiple of thewavelength of the operating frequency of the power source 213. Due tothe velocity inhibited nature of the power multiplying network 203, itssize is quite compact in comparison with the wavelength of the operatingfrequency of the power source 213. In addition, the direction coupler209 causes a phase shift that is equal to one quarter of the wavelengthof an exciting traveling wave generated by the power source 213 at theoperating frequency as will be discussed.

In one embodiment, the power multiplying network 203 is constructed fromlumped-elements 216 such as, for example, the inductances L andcapacitances C as shown in FIG. 8. In one embodiment, the inductances Lmay be actual inductors and the capacitances C may be actual capacitorsthat are either commercially available or may be constructed as needed.For example, the power multiplying network 203 may be characterized as aring of interconnected T-networks 183 a (FIG. 7A) or π-networks 186 a(FIG. 7B), although the interconnected T-networks 183 a (FIG. 7A) orπ-networks 186 a (FIG. 7B) may be arranged in a multiply-connectedstructure other than a ring. Each of the T-networks 183 a or π-networks186 a may be considered a “section” of the power multiplying network203. In this respect, assuming that the power multiplying network 203comprises a number of T-networks 183 a, then each inductance L may bedivided into two series inductances L/2 that make up the seriesinductances L/2 as described in the T-network 183 a (FIG. 7A).Similarly, assuming that the power multiplying network 203 comprises anumber of π-networks 186 a, each capacitance C may be also be viewed asa pair of shunt capacitances C/2, each such shunt capacitance C/2 makingup one of the shunt capacitances C/2 of the π-network 186 a (FIG. 7B).Whether T-networks 183 a or π-networks 186 a are employed to create thesections of the power multiplying network 203, each of the networks 183a or 186 a results in a predefined phase shift φ_(S).

Assuming that either T-networks 183 a or π-networks 186 a are to beemployed to construct the power multiplying network 203 at somefrequency f and some quality factor Q, then values for the lumpedelements 216 such as the inductances L and capacitances C or otherlumped elements are determined. The quality factor Q is definedconventionally asQ=f/Δf.

Such values may be calculated from the known characteristic impedanceZ_(o) and the transmission line complex propagation constant γ of apredetermined portion of the hypothetical transmission line 101 (FIG. 3)of the hypothetical power multiplier 100 a. In this respect, thecharacteristic impedance Z_(o) and the transmission line complexpropagation constant γ may be calculated for a predefined unit length ofthe hypothetical transmission line 101 as follows: $\begin{matrix}{{Z = {R_{T} + {{j\omega}\quad L_{T}}}},} \\{{Y = {G_{T} + {{j\omega}\quad C_{T}}}},} \\{Z_{o} = \sqrt{Z/Y}} \\{{= \sqrt{\left( {R_{T} + {{j\omega}\quad L_{T}}} \right)/\left( {G_{T} + {{j\omega}\quad C_{T}}} \right)}}\quad,\quad{and}} \\{\gamma = \sqrt{ZY}} \\{{= \sqrt{\left( {R_{T} + {{j\omega}\quad L_{T}}} \right)\left( {G_{T} + {{j\omega}\quad C_{T}}} \right)}},}\end{matrix}$where Z is the series impedance per unit length of transmission line, Yis the shunt admittance per unit length of transmission line. In the lowloss case (i.e. R_(T)≈0 and G_(T)=0), the characteristic impedancereduces toZ _(o) =√{square root over (L_(T)/C_(T))}.In addition, the velocity of propagation may be calculated as$v = {\frac{1}{\sqrt{L_{T}C_{T}}}.}$

In order to determine values for R_(T), L_(T), G_(T), and C_(T), for agiven section of transmission line 159, various references may beconsulted that provide such information such as, for example, Terman, F.E., Radio Engineering Handbook, McGraw-Hill, 1943, pp. 172-178, 191-215,or other references as can be appreciated.

Once the characteristic impedance Z_(o) for a predefined portion of thehypothetical transmission line 101 is known, then the complex electricallength θ of the predefined portion of the hypothetical transmission line101 is calculated asθ=γ1where l is the physical length of the predefined portion of thehypothetical transmission line 101. Given the characteristic impedanceZ_(o), the transmission line complex propagation constant y, and theelectrical length θ of the predefined portion of the hypotheticaltransmission line 101, the series impedances Z₁ and Z₂, and the shuntimpedance Z₃ of the T-network 183 (FIG. 6A) may be calculated asfollows:Z ₁ =Z ₂ =Z _(o) tan h(θ/2), andZ ₃ =Z _(o)/sin h(θ).

Alternatively, the shunt impedances Z_(A) and Z_(B), and the middleimpedance Z_(C) of the π-network 186 may be calculated as follows:Z _(A) =Z _(B) =Z _(o) cot h(θ/2), andZ_(C)=Z_(o) sin h(θ).

Once the series impedances Z₁ and Z₂, and the shunt impedance Z₃ of theT-network 183, or the shunt impedances Z_(A) and Z_(B), and the middleimpedance Z_(C) of the π-network 186 are known, then correspondingvalues for L and C may be determined. Assuming, for example, that onehas calculated the shunt impedances Z_(A) and Z_(B), and the middleimpedance Z_(C) of the π-network 186, then inductance L associated withthe middle impedance Z_(C) may be calculated therefrom whereZ _(C) =r+jωL.

Also, the capacitance C associated with the shunt impedances Z_(A) andZ_(B) may be calculated whereZ _(A) =Z _(B)1/jωC.

It may be the case that L and C are too large to be practicallyrepresented in the form of a lumped element 216. If such is the case,then a reverse calculation or reverse mapping may be performed usingknown values for L and C to determine how much of the hypotheticaltransmission line 101 may be represented by a given T-network 183 orπ-network 186. In this respect, one may determine how many T-networks183 or π-networks 186 may necessarily be employed in a given powermultiplying network 203. In this respect, values may be chosen for L andC in view of the calculated values for L and C identified above.

Assuming that the series impedances Z₁ and Z₂, and the shunt impedanceZ₃ of the T-network 183 are calculated from predetermined values for Land C, then the characteristic impedance Z_(o) and the transmission linecomplex propagation constant γ0 may be calculated as follows:$\begin{matrix}{{Z_{o} = \sqrt{Z_{1}\left( {Z_{1} + {2Z_{3}}} \right)}},{and}} \\{\gamma = {{Arc}\quad{{\tanh\left( \frac{\sqrt{Z_{1}\left( {Z_{1} + {2Z_{3}}} \right)}}{Z_{1} + Z_{3}} \right)}.}}}\end{matrix}$

Alternatively, assuming that the shunt impedances Z_(A) and Z_(B), andthe middle impedance Z_(C) of the π-network 186 are calculated frompredetermined values for L and C, then the characteristic impedanceZ_(o) and the transmission line complex propagation constant γ may becalculated as follows: $\begin{matrix}{{Z_{o} = {Z_{A}\sqrt{\frac{Z_{C}}{Z_{C} + {2Z_{A}}}}}},{and}} \\{\gamma = {{Arc}\quad{{\tanh\left( \frac{\sqrt{Z_{C}\left( {Z_{C} + {2Z_{A}}} \right)}}{Z_{A} + Z_{C}} \right)}.}}}\end{matrix}$

Once the length I of the hypothetical transmission line 101 that isrepresented by a specified T-network 183 or π-network 186 is known, thenone can determine how many similar T-networks 183 or π-networks 186 areneeded to simulate the impedance of the entire hypothetical transmissionline 101. Thus, by performing the forward and reverse calculationsdescribed above, one can determine general values for the inductances Land capacitances C of the power multiplying network 203.

In addition, the power multiplying network 203 further comprises a phaseshifter 219. The phase shifter 219 comprises a circuit constructed fromlumped-elements that is combined in series with a portion of thedirectional coupler 209 to make up the inductance L of the specificsection within which the directional coupler 209 is located.

The power multiplying network 203 also includes a diverter 223 thatcouples the power multiplying network 203 to a load 226. The diverter223 is defined herein as an electrical element or circuit that may beemployed to divert or redirect all or a portion of a traveling wave fromthe power multiplying network 203 to the load 226. In this respect, thediverter 223 may comprise, for example, a switch, relay, solid stateswitch, plasma switch, or other device with like capability. Thediverter 223 may also be a circuit that presents an electric window thatis biased using a predefined control voltage or current to divert theenergy within a traveling wave to the load 226, depending upon the stateof the control voltage or current, etc.

During operation, the power source 213 is employed to launch an excitingtraveling wave in the launching network 206. The exciting traveling wavemay be, for example, a sinusoidal wave or other appropriate shape. Thedirectional coupler 209 couples at least a portion of the excitingtraveling wave from the launching network 206 into the power multiplyingnetwork 203, thereby resulting in a traveling wave that propagateswithin the power multiplying network 203. Given that the electricallength of the power multiplying network 203 is an integer multiple ofthe wavelength of the power source 213 and that the directional coupler209 is equal to ¼ of the wavelength of the power source 213, then thetraveling wave that propagates within the power multiplying network 203is continually reinforced by the portion of the exciting traveling wavethat is coupled into the power multiplying network 203. Also, thetraveling wave propagates in a single direction around the powermultiplying network 203. This results in power magnification M of thepower of the traveling wave by a predefined factor that may be manytimes greater than the power of the power source 213, depending upon thelosses and tolerances of the lumped-elements 216 and other factors.

Both the exciting traveling wave launched into the launching network 206and the traveling wave that propagates around the power multiplyingnetwork 203 may be AC power signals such as electrical power signalsgenerated at 50 Hertz, 60 Hertz, 400 Hertz, or any other power frequencyas can be found in the electrical generation systems in the UnitedStates and countries around the world. However, in any event, thefrequency of the exciting traveling wave, the traveling wave, and thepower source 213 may be any frequency possible, although they typicallycorrespond to frequencies with wavelengths for which the closed pathlength of the power multiplying network 203 is approximately 1/10 thewavelength or less of the traveling wave.

When the exciting traveling wave is applied to the launching network206, the power of the traveling wave continually increases with timeuntil it reaches a maximum power. The maximum power is reached when thelosses in the power multiplying network 203 plus the losses in thematching load R_(L) are equal to the power supplied by the power source213. When the maximum power is reached, the diverter 223 may be actuatedto direct the traveling wave from the power multiplying network 203 tothe electrical load 226. In a typical situation, it may take up toapproximately a dozen cycles to reach maximum power in the powermultiplying network 203, although it is possible that maximum power maybe reached in more or less cycles. Alternatively, the diverter 223 maybe actuated to direct the traveling wave from the power multiplyingnetwork 203 at any time deemed appropriate such as, for example, whenthe energy accumulated in the power multiplying network 203 reaches anypredefined threshold, etc.

The power multiplier 200 provides significant advantages in that itfacilitates real power multiplication at lower power frequencies such asthe operating frequencies of electrical power distribution systemsaround the world that operate, for example, at 50 Hertz, 60 Hertz, 400Hertz, or other low frequencies. The velocity inhibiting nature of thepower multiplying network 203 facilitates the creation of a powermultiplier 200 that can operate at such low power generation frequencieswith astonishing size reduction. That is to say, where prior theory mayhave taught that power multipliers operating at conventional powergeneration frequencies might have required a hypothetical waveguide thatextended for thousands of kilometers as discussed with reference to FIG.3, now the same can be created in a compact size that fits, for example,in a small room.

The velocity of propagation of the traveling wave through the powermultiplying network 203 relative to the velocity of a traveling wavethrough free space is described herein as the velocity factor. Thevelocity inhibiting nature of the power multiplying network 203 providesfor velocity factors that are on the order of 1/1,000,000, although evensmaller velocity factors may be achieved.

In addition, the power multiplier 200 may further include a number oflaunching networks 206, each launching network 206 being coupled to thepower multiplying network 203 by a directional coupler 209. Such aconfiguration would facilitate a corresponding increase in the rate atwhich the power of the traveling wave accumulates during operation ofthe power multiplier 200.

In an alternative embodiment, the traveling wave may be a solitary wavethat propagates around the power multiplying network 203. In order topropagate a solitary wave around the power multiplying network 203, thepower multiplying network 203 is constructed so as to include nonlinearelements such as, for example, diodes, transistors, or other activecomponents so as to be nonlinear and dispersive. Thus, nonlinearcomponents are defined herein as components that provide an outputhaving an amplitude that is not linearly proportional to the input ascan be appreciated by those with ordinary skill in the art. Byconstructing the power multiplying network 203 from a suitable networkof nonlinear elements and/or a combination of linear and nonlinearelements, a solitary wave may be propagated around the power multiplyingnetwork 203. In this respect, the power source 213 would be a pulsegenerator that generates and launches an exciting traveling wave intothe launching network 206. To achieve power multiplication, a solitaryexciting traveling wave would have to be spatially synchronized with thesolitary traveling wave. In addition, the launching network 206, thedirectional coupler 209, and the phase shifter 219 may be constructed toinclude elements that are nonlinear and dispersive in nature tofacilitate the propagation of solitary waves there through.

It should be appreciated that as the gain of the power multiplyingnetwork 203 increases, its quality factor Q rises and its bandwidth BWnarrows around the operating frequency. In one embodiment, this may be adesirable asset for a strictly monochromatic system. Should broaderbandwidths BW be desired, the electrical bandwidth BW of the powermultiplying network 203 may be tailored for the specific application.For example, low-loss power multiplying networks 203 with broader andcontrolled-shape passbands may be constructed following variouselectrical filter design. See for example, Matthaei, G. L., L. Young,and E. M. T. Jones, Microwave Filters, Impedance Matching Networks, andCoupling Structures, McGraw-Hill, 1964; and Fano, R. M., TheoreticalLimitations on Broadband Matching of Arbitrary Impedances, Journal ofthe Franklin Institute, Vol. 249, 1950, pp. 53-83 and 129-155.

In another embodiment, the power multiplier 200 as described above mayalso be constructed incorporating so called “Tracking-Filter” designtechniques such that the electrical passband of the power multiplier 200can be dynamic and automatically controlled to coherently trackfrequency and phase variations of the power source 213 while maintainingthe desired operational properties described above. In implementing apower multiplier 200 with a dynamic electrical passband, the frequencyof the power source 213 is monitored and compared with the resonantfrequency of the power multiplying network 203. An error signal may begenerated from such a comparison and employed in a feedback loop todynamically modify the ring component parameters such as thelumped-elements of the power multiplying network 203 to tune it to thespectral variations of the power source 213. In such case, thelumped-elements described above may be parametrically dynamic withvariable parameters as can be appreciated.

Referring next to FIG. 9, shown is a schematic that provides one exampleof the phase shifter 219 according to an aspect of the presentinvention. The phase shifter 219 comprises a T-network 183 a (FIG. 7A),although a π-network 186 a may be employed as well. In this respect, thephase shifter 219 includes series inductances L_(T) and a shuntcapacitance C_(T). In this respect, the phase shifter 219 is constructedfrom lumped-elements as part of the power multiplying network 203.

The series inductances L_(T) and the shunt capacitance C_(T) arespecified so as to result in a phase shift φ_(S). The series inductancesL_(T) and/or the shunt capacitance C_(T) (assuming that a T-network 186a is employed) may be variable so as to allow the phase shift φ_(S) tobe adjusted as necessary to compensate for any inaccuracies in the phaseshifts φ_(S) of each section and in the phase shift θ of the directionalcoupler 209. This is done to ensure that the total phase shift presentedby the power multiplying network 203 is an integer multiple of 360degrees for the wavelength of the power source 213. The specificcalculations that are performed to determine the values of theinductances L_(T) and the shunt capacitance C_(T) will be discussed.

With reference to FIG. 10, shown is a schematic that illustrates anexample of the directional coupler 209 according to an aspect of thepresent invention. The directional coupler 209 comprises a number oflumped-elements. Such a directional coupler 209 ensures that thetraveling wave propagates in a single direction along the powermultiplying network 203 and to achieve the reinforcement of thetraveling wave with the portion of the exciting traveling wave thatpropagates through the launching network 206.

With the foregoing discussion of the power multiplying network 203, thedirectional coupler 209, and the phase shifter 219, the total phaseshift presented by the power multiplying network 203 may be determinedas follows:φ_(PMW)=φ_(s)(N−1)+φ+θ,where N is equal to the number of sections in the power multiplyingnetwork 203.

In addition, the diverter (FIG. 8) may be constructed in a mannersimilar to the directional coupler 209 in which the values of thecoupling capacitances are used to control the rate at which energyexists the power multiplying network 203.

Referring next to FIG. 11, shown is a schematic of a power multiplier250 according to another embodiment of the present invention. The powermultiplier 250 includes a power multiplying network 253 that isconstructed from a toroidal helix as shown, or any of its variantscomprising left handed, right handed, or superpositions of left andright handed helices as taught by Canadian Patent 1,186,049, U.S. Pat.No. 4,622,558, and U.S. Pat. No. 4,751,515, each of these referencesbeing filed by James F. Corum, the entire text of each of thesereferences being incorporated herein by reference. In this respect, thetoroidal helix includes the inductances L (FIG. 8) by virtue of itsconstruction. In addition, the impedance presented by the toroidal helixincludes capacitances as can be appreciated by those with ordinary skillin the art. (see Krause, John D., Antennas, McGraw-Hill, 1^(st) edition,1950, FIG. 7.2). The power multiplier 250 includes a launching network256 that is coupled to the power multiplying network 253 by adirectional coupler 259. The power multiplier 250 also includes thediverter 223 that couples an output from the power multiplier 250 to aload 226 as shown. The power source 213 is coupled to the launchingnetwork 256 and launches an exciting traveling wave into the launchingnetwork 256 in a similar manner as was described with reference to thepower multiplier 200. Similarly, the launching network 256 is terminatedin a matching load R_(M).

The directional coupler 259 may be, for example, a section of the helixor even a π-network 186 (FIG. 7B) as shown. The directional coupler 259imposes a phase shift of ¼ of the wavelength of the exciting travelingwave in a similar manner as was described above.

The operation of the power multiplier 250 is substantially similar aswas discussed with reference to the power multiplier 200 of FIG. 8. Thepower multiplier 250 illustrates that fact that the power multiplyingnetwork 253 may comprise one or more electrical structures such as atoroidal helix, two or more cross-wound helices, a contrawound helix, orother electrical structures that include inherent capacitances andinductances that act as the lumped elements 216 (FIG. 8) such as theinductances L (FIG. 8) and capacitances C (FIG. 8).

With reference back to FIG. 8, once we have determined the values forthe inductances L and capacitances C per section of the power multiplier200 that comprises T-networks 183 (FIG. 6A) or π-Networks 186 (FIG. 6B),then actual power magnification that can be achieved by the resultingpower multiplier 200 given the values for the lumped-elements (i.e. theshunt capacitances C and the series inductances L) may be determined.Specifically, the lumped-elements are specified to achieve a predefinedphase shift per section at the predefined operating frequency.

The progression of calculations that is performed to determine thevalues for the lumped elements 216 such as the capacitances C andinductances L of the power multiplier 200 is now discussed. In thefollow calculations, the assumption is made that each section of thepower multiplying network 203 comprise π-networks 186 (FIG. 6B). Tobegin, the operating frequency f of the power multiplier 200 isspecified. Also, both the inductance L and capacitance C of each sectionof the power multiplying network 203 are specified based upon the valuesfor such elements identified above. In addition, a quality factor Q isspecified for the inductances L of each section of the power multiplyingnetwork 203. The frequency in terms of radians/sec is calculated asω=2πf radians/sec.

Also, the resistance in each of each inductance L is calculated as$r = {\frac{\omega\quad L}{Q}{{Ohms}.}}$

Thereafter, the impedance Z_(C) is calculated as follows:Z _(C) =r+iωL Ohms,where “i” represents √{square root over (−1)} as is known by those withordinary skill in the art. Given the capacitances C specified above, theshunt impedances Z_(A) and Z_(B) are calculated as follows:$Z_{A} = {Z_{B} = {\frac{1}{{\mathbb{i}}\quad\omega\quad C}{{Ohms}.}}}$

Next, the characteristic impedance Z₀ is calculated as follows:$Z_{0} = {Z_{A}\sqrt{\frac{Z_{C}}{\left( {Z_{C} + {2Z_{A}}} \right)}}{{Ohms}.}}$The characteristic impedance is defined as the ratio of the forward wavevoltage over the forward wave current. In this respect, a physicalmeasurement of the characteristic impedance of each section may be takenand compared with the calculated characteristic impedance Z₀ to verifythe accuracy thereof.

In addition, the propagation constant y per section is calculated asfollows:$\gamma = {a\quad{{\tanh\left\lbrack \frac{\sqrt{Z_{C}\left( {Z_{C} + {2Z_{A}}} \right)}}{\left( {Z_{A} + Z_{C}} \right)} \right\rbrack}.}}$

The Attenuation Constant α per section and the Phase Constant β persection are defined asα_(section)=Re(γ) Nepers/section, andβ_(section)=Im(γ) radians/section.

The phase shift per section may then be calculated asφ=(57.296 Deg/Rad)β_(section) Degrees.

The velocity of the traveling wave in sections per second propagatingalong the power multiplying network 203 is calculated as$v = {\frac{\omega}{\beta_{section}}\quad{sections}\text{/}{{second}.}}$

Next, the electrical circumference C_(λ) of the power multiplyingnetwork 203 is specified in terms of wavelengths at the operatingfrequency in degrees asC_(Deg)=C_(λ)(360 Degrees/wavelength) Degrees.

Next, the number of sections N (either T-networks or π-networks) iscalculated as $N = {\frac{C_{Deg}}{\phi}.}$

Once the number of sections N is known, then the loss resistance R_(C)around the closed path of the power multiplying network 203 may becalculated asR_(C)=Nr Ohms.where r is as defined above. The field propagation decay A for a singletraversal of the power multiplying network 203 may be calculated asA=e^(−α) ^(section) ^(N).

The attenuation AdB around the power multiplying network 203 iscalculated asA_(dB)=−20 log(A).

The pulse duration T of a peripheral disturbance is calculated as$\tau = {\frac{N}{v}\quad{{seconds}.}}$

The power magnification M of the power multiplier 200 at optimumcoupling is calculated as $M = {\frac{1}{\left( {1 - A^{2}} \right)}.}$

The power magnification M_(dB) expressed in decibels is calculated asM_(dB)=10 log(M).

The optimum coupling C_(opt) is calculated asC _(Opt)=1−A ².

The optimum coupling C_(opt) is calculated in decibels (dB) asC_(optdB)=10 log(C_(opt) dB.)

In addition, a useful reference that may be consulted to determine thevarious elements of the directional coupler 209 and the phase shifter219 is Matthaei, G. L., L. Young, and E. M. T. Jones, Microwave Filters,Impedance Matching Networks, and Coupling Structures, McGraw-Hill, 1964,(see Chapter 14). While specific circuit designs may be discussed hereinthat may be employed as the directional coupler 209 and the phaseshifter 219, it is understood that other circuit designs and circuitstructures may be employed as well, such alternative designs fallingwithin the scope of the present invention.

Referring next to FIG. 12, shown is the power multiplier 200 coupled toa power distribution network 300 according to one embodiment of thepresent invention. While the power multiplier 200 that employs the powermultiplying network 203 is shown in FIG. 12, it is understood that otherembodiments of power multipliers as described herein such as the powermultiplier 250 may be employed, where the power multiplier 200 and thepower multiplying network 203 are described herein merely as an example.

The power distribution network 300 may be, for example, a power gridsuch as the North American power grid or other power grids anywhere inthe world. As shown in FIG. 12, the launching network 206 is coupled tothe power distribution network 300. The output of the diverter 223 isalso coupled to the power distribution network 300.

The diverter 223 receives a load feedback 303 that may comprise, forexample, a load feedback signal generated based upon a currentelectrical load on the power distribution network 300. The directionalcoupler 209 may be selectively coupled to the launching network 206, orthe launching network 206 may be selectively coupled to the powerdistribution network 300 in order to facilitate a controlled power inputinto the power multiplying network 203 from the power distributionnetwork 300, thereby resulting in storage of power in the powermultiplying network 203 of the power multiplier 200. Alternatively, thedirectional coupler 209 may be configured to control the rate at whichpower is input into the power multiplying network 203. By virtue of thefact that the launching network 206 and the diverter 223 are bothcoupled to the power distribution network 300, the power multiplyingnetwork 203 may be employed to store power from the power distributionnetwork 300 and to supply power to the power distribution network 300 asdesired.

The diverter 223 may be configured to control the output of the powermultiplying network 203 in response to the load feedback 303. In thisrespect, the power stored in the power multiplying network 203 may besupplied, for example, to the power distribution network 300 to providepower upon an occurrence of an abrupt increase in the electrical loadassociated with the power distribution network 300.

Given that utilities that supply power to power distribution networks300 can experience severe mismatches between peak and average loaddemands, the power multiplying network 203 may advantageously beemployed for “power smoothing.” For example, the power multiplyingnetwork 203 may be employed in locations local to electrical loads thatmay be remote from power generation stations to “smooth” brown outs andblack outs by utilities with large peak-to-average load demands. In thisrespect, the power multiplying network 203 may be coupled to variouslocations of power distribution networks 300 to provide local controlledsmooth transition between load states by providing for temporary energystorage that may be drawn upon as needed.

This may reduce the electro-mechanical stress on existing powergeneration equipment in electrical generation stations. Specifically,when large load swings and transients occur on the power distributionsystems 300, significant electromechanical stresses can occur inrotating machinery used in power generation. For example, either a onetime occurrence of a large transient or the repeated occurrences ofsmaller transients over time can result in the catastrophic failure ofshafts and other mechanical components of electrical generators. Also,electrical wiring failure can occur in generators and at other points inelectrical distribution systems. In addition, load swings and transientscan affect the frequency and phase stability of electrical generators asthey react to the changes in electrical loads. The power multiplyingnetwork can be employed to eliminate such stresses on power generationand distribution equipment, and can ensure frequency and phase stabilityin the existing power distribution networks 300.

In circumstances where there exists an intervening electrical load pointsuch as a city between electrical generation stations and a remote load,it is possible that during heavy load times, the demanded throughputcannot be conveyed from the electrical generation station to the remoteload through the intervening electrical load point. Thus, a powermultiplier 200 that includes the power multiplying network 203, forexample, may be employed to address the “rush hour” electrical trafficcongestion problem around such intervening load point. For example, thepower multiplying network 203 may be coupled to the power distributionnetwork 300 near the intervening load point to provide for storage ofpower that can be accessed at such heavy traffic times, thus smoothingthe demand and preventing loss of service at the remote load.

To facilitate effective power smoothing on a given power distributionnetwork 300, one or more power multiplying networks 203 may be coupledto demand stressed portions of a given power distribution network 300.As described above, such demand stressed portions of a powerdistribution network 300 may be at locations near cities or other largeloads that experience large peak-to-average load demands. Also, suchdemand stressed portions may be near intervening electrical load points.Additionally, other locations of various power distribution networks 300may be demand stressed as will be appreciated.

The various embodiments of the power multipliers described herein,including the power multiplier 200 employing the power multiplyingnetwork 203, are ideal for power smoothing on a power distributionnetwork 300 since the power stored in such power multiplying networks isavailable on a near instantaneous basis. Consequently, the powermultiplying network 203 may be employed, for example, to supply powerwhen generating equipment on the power distribution network 300 cannotreact fast enough to compensate for abrupt changes such as increases inthe electrical load. In this respect, one or more power multiplyingnetworks 203, for example, may be employed to supply power to the powerdistribution network 300 for periods of time to facilitate theadjustment of power generation systems coupled to the power distributionnetwork to supply power to the increased electrical load after theoccurrence of the abrupt increase.

With reference to FIG. 13, shown are several power multipliers 200/250that employ power multiplying networks 203/253 coupled to the powerdistribution network 300 according to another embodiment of the presentinvention. While the power multiplying networks 203/253 are shown, otherembodiments of the power multiplying networks may be employed as can beappreciated. A power multiplier control system 206 is provided withoutputs that are electrically coupled to each of the diverters 223 ofthe respective power multipliers 200/250.

The power multiplier control system 206 generates control outputs thatare applied to the diverters 223 to control the release of power fromeach of the power multiplying networks 203/253 to the power distributionnetwork 300 in response to the load feedback from the power distributionnetwork 300. In one embodiment, the power multiplier control system 206is configured to apply power from each of the power multiplying networks203/253 to the power distribution network 300 in a sequential order. Inthis respect, the period of time that the power distribution network 300may be supplied with power from the power multiplying networks 203/253is increased based upon the number of power multiplying networks 203/253employed. In this respect, multiple power multiplying networks 203/253may be employed to provide adequate time for generating equipment toadjust to changing electrical loads without stressing the mechanical andelectrical components of the generating equipment. Alternatively, thepower stored in multiple ones of the power multiplying networks 203/253may be applied to the power distribution network 300 concurrently tomeet extreme load increases.

Furthermore, the elements that are employed to construct the variousembodiments of the power multiplying networks 203/253 described hereinmay be constructed using low loss and high permittivity dielectrics incapacitances, and low loss conductors in the inductances (such asinductance coils). Such low loss conductors may be, for example,cryogenic conductors and/or superconductors. Such low loss conductorsallow for much greater storage capacity at extremely high efficiencies.Specifically, given that power storage will increase in the powermultiplying networks 203/253 as described herein until the lossesexperienced in the power multiplying networks 203/253 equal the powerinput, where a given power multiplying network is constructed ofextremely low loss conductors, it follows that very large amounts ofpower may be stored.

Power Multiplication and Parametric Excitation

With reference to FIGS. 14 and 15, shown are drawings of powermultipliers 400 a and 400 b that employ parametric excitation accordingto various embodiments of the present invention. The power multipliers400 a and 400 b each include a respective power multiplying network 403a and 403 b and a launching network 406. Each of the power multiplyingnetworks 403 a/403 b comprises a ring as mentioned above. The launchingnetwork 406 also includes a directional coupler 409 that couples thelaunching network 406 to the respective power multiplying networks 403a/403 b. A power source 413 is coupled to the launching network 406.Also, the launching network 406 is terminated in a matching load R^(L).

In addition, the each of the power multiplying networks 403 a/403 bfurther comprises a phase shifter 419. The phase shifter 419 comprises acircuit constructed from lumped-elements that is combined in series witha portion of the directional coupler 409 to make up the inductanceL(t)/L of the specific section within which the directional coupler 409is located.

Each of the power multiplying networks 403 a/403 b also includes adiverter 423 that couples the respective power multiplying network 403a/403 b to a load 426. The diverter 423 is defined herein as anelectrical element or circuit that may be employed to divert or redirectall or a portion of a traveling wave from one of the power multiplyingnetworks 403 a/403 b to the load 426. In this respect, the diverter 423may comprise, for example, a switch, relay, solid state switch, plasmaswitch, or other device with like capability. The diverter 423 may alsobe a circuit that presents an electric window that is biased using apredefined control voltage or current to divert the energy within atraveling wave to the load 426, depending upon the state of the controlvoltage or current, etc.

In the embodiment shown in FIGS. 14 and 15, each of the powermultiplying networks 403 a/403 b is constructed from reactances 416 andparametric reactances 418 that, according to one embodiment, compriselumped-elements. As shown in FIG. 14, the reactances 416 comprisecapacitances C (FIG. 14) and inductances L (FIG. 15) and the parametricreactances 418 comprise parametric inductances L(t) (FIG. 14) andparametric capacitances C(t). Alternatively, the parametric reactances418 in a single power multiplier may include both parametric inductancesL(t) and parametric capacitances C(t).

In one embodiment, the parametric reactances 418 such as the parametricinductances L(t) or the parametric capacitances C(t) may comprise linearor non-linear reactances. Thus, the parametric inductances L(t) maycomprise linear or non-linear inductances and the parametriccapacitances C(t) may comprise linear or non-linear capacitances. Asdescribed herein, a linear circuit component is one in which theimpedance of the circuit component is not a function of the magnitude ofa voltage signal in the circuit component.

Examples of linear reactances may comprise, for example, conventionalair-core coils of wire, capacitors, and similar lossless passive circuitelements composed of media with linear permeability (μ) and lineardielectric permittivity (∈). Sections of transmission lines (andwaveguides) constructed of linear media may also supply examples oflinear reactances as viewed at their inputs.

Examples of non-linear reactances may comprise reactive elements with anonlinear impedance relationship between voltage and current. Suchreactive elements may include saturable reactors, varactor (varicap)diodes with voltage variable junction capacitance, and elementsconstructed of nonlinear permittivity [∈=∈(V), where permittivity is afunction of voltage] or nonlinear permeability [μ=μ(I), wherepermeability is a function of current], as is the case in transmissionline elements with magnetically biased ferrites, and even plasma media.

Time-varying reactive elements also occur in engineering practice.Common examples of time-varying reactances are inductors and capacitorswhose permittivity and permeability functions are pumped in time by acontrol voltage or current. Similarly, distributed time-varyingimpedances have their constitutive parameters pumped by a controlsignal, which may be electrical, electromagnetic, optical, thermal,mechanical, acoustical, etc.

The power multipliers 400 a and 400 b are operated in order to multiplypower in much the same way as the power multipliers 200 (FIG. 8) or 250(FIG. 11) with the exception that the parametric reactances 418 arevaried in time as will be described below. As a result of the variationof the parametric reactances 418, a negative resistance is introducedinto the power multiplying networks 403 a/403 b that effectivelyelectrically negates the physical resistance inherent in the componentsof the power multiplying networks 403 a/403 b. Consequently, the powermultipliers 400 a/400 b can accumulate a drastically greater amount ofpower in a traveling wave within the power multiplying networks 403a/403 b. In the case that the physical resistance of a respective powermultiplying network 403 a/403 b is almost completely negated, then thepower multiplying network 403 a/403 b may actually approachsuperconductivity.

Recall as described above that in a power multiplier 200 (FIG. 8) thatdoes not employ parametric excitation (does not make use of parametricreactances), power will continue to build up in the power multiplyingnetwork 203 (FIG. 8) (or the ring) during operation until the losses dueto the inherent resistance of the power multiplying network 203 plus thelosses in the matching load RL that terminates the launching waveguide406 is equal to the power generated by the power source 413. Given theuse of parametric reactances 418 in the power multiplying networks 403a/403 b, the physical resistance of the power multiplying networks 403a/403 b are negated by the negative resistance introduced due to theparametric excitation of the parametric reactances.

Thus, if the physical resistance was reduced due to the negativeresistance injected in the power multiplying networks 403 a/403 b, thepower of the traveling wave in the power multiplying networks 403 a/403b will continue to build up until the losses due to the reduced physicalresistance and due to the matching load equal the power generated by thepower source 413. As the negative resistance injected into a powermultiplying network 403 a/403 bapproaches the total physical resistanceof a respective one of the power multiplying networks 403 a/403 b, thenthe power multiplying networks 403 a/403 b approach superconductivity.However, it may be the case that there are limits to how closely thenegative resistance can approach the actual physical resistance of therespective power multiplying network 403 a/403 b, where the actualamount of negative resistance depends upon the magnitude and phase ofthe variation in the parametric reactances that make up part of thepower multiplying network 403 a/403 b. Thus, the actual amount ofnegative resistance generated is application specific.

According to the various embodiments, one or more parametric reactances418 in the power multiplying networks 403 a/403 b are varied in time ata frequency that is in a predefined relationship relative to theoperating frequency of the power source 413. That is to say, thefrequency of at which the parametric reactances 418 are varied in timeis in a predefined relationship relative to the frequency of a travelingwave in the ring of the power multiplier 400 a/400 b.

To explain further, if a signal at frequency f_(s) is injected into alinear, tuned circuit such as an LC circuit, which has a reactiveelement changing at frequency f_(p) (called the “pump” frequency), a newmixer frequency (called the idler frequency, fi) will appear in thecircuit. The relation between these three frequencies is as follows:f _(i) =mf _(p) ±nf _(s).

If the reactance element is varied at a frequency f_(p) (the pumpfrequency) in a 2:1 ratio to the resonant frequency (which is also tunedto the signal frequency f_(s)) of the circuit, then the difference oridler frequency f_(i) will be the same as the signal frequency f_(s).

If the operating point of the reactance element is varied at onefrequency, and an oscillator signal is coupled into the circuit atanother frequency, under certain conditions between the two frequencies,the circuit impedance, instead of being a pure imaginary, will becomecomplex. The imaginary component could correspond to an inductivereactance, but a negative real part can arise, effectively correspondingto a negative resistance injected into the circuit. The amount ofnegative resistance injected into the circuit is controlled by therelative magnitude and phase at which the reactance element is varied.

According to various embodiments, the negative resistance arises whenthe pump frequency f_(p) is equal to twice the signal frequency f_(s) ofthe circuit. In this “degenerate” mode of operation, where both m andn=1 and f_(p)=2×f_(s), the idler frequency f_(i) is equal to the signalfrequency f_(s). Therefore, when the pump frequency f_(p) is equal totwice the signal frequency (2×f_(s)), a negative resistance is injectedinto the circuit.

According to the various embodiments of the present invention, which, bydesign, possess small dissipation, the parametric reactances 418 arevaried at a frequency that is twice the frequency of the power source413 (and the generated traveling wave flowing through the ring) of thepower multiplier 400 a/400 b. When this condition is met, the parametricreactance effectively negates at least a portion of the physicalresistance inherent in the power multiplying networks 403 a/403 b. Thedegree to which the physical resistance inherent in the powermultiplying networks 403 a/403 b is negated depends upon the magnitudeof the negative resistance generated by the operation of the parametricreactances. The magnitude of the negative resistance depends upon themagnitude and phase of the variation of the parametric reactances 418and is design specific as described above.

While, in one embodiment, a ratio of 2:1 is specified between thefrequency of variation of the parametric reactances 418 and thefrequency of the power source 413 (or traveling wave in the ring) inorder to generate the negative resistance in the power multiplyingnetworks 403 a/403 b, it is understood that other frequencyrelationships between the frequency of variation of the parametricreactances 418 and the frequency of the power source 413 may bespecified in order to generate the negative resistance in the powermultiplying networks 403 a/403 b. For example, to aid in determiningsuch other frequency relationships between the frequency of variation ofthe parametric reactances 418 and the frequency of the power source 413,see the topic of Mathieu's Equation in Cunningham, W. J., Introductionto Nonlinear Analysis, McGraw-Hill, 1958, pp. 259-280) on circuitdissipation.

As Cunningham demonstrates, growing oscillations (negative resistance)and regions of instability may occur in second order systems for certainother noninteger (i.e. not commensurable) frequency ratios, which, inthe presence of damping, also depend upon system dissipation as well asthe amplitude and phase of the parameter variation. These are commonlymanifested as the region of instability “tongues” in the solutions ofMathieu's equation. Also, see Kharkevich, A. A., Nonlinear andParametric Phenomena in Radio Engineering, John F. Ryder Publisher,Inc., 1962, pp. 166-166; Mandelshtam, L. I. and Papaleksi, N. D., “Onthe Parametric Excitation of Electric Oscillations,” Soviet Journal ofTechnical Physics, Vol. 4, No. 1, 1934, pp. 5-29. See FIG. 1, p. 9.)Such other frequencies may also be employed, although efficiency maysuffer at such other ratios.

The parametric reactances 418 may be implemented using any one of anumber approaches. In particular, the parametric reactances 418 may becreated electrically, mechanically, thermally, or via some otherapproach. Specific examples include the creation of a parametricinductance L(t) using a magnetic amplifier that involves varying thepermeability p of a core about which an inductor is wound. As thepermeability p is altered, so is the inductance of the winding. Also, inanother example, the parametric capacitance C(t) may be created using adielectric amplifier in which the permittivity ∈ of a dielectricassociated with the parametric capacitance C(t) is varied over time. Asthe permittivity ∈ is varied, the resulting capacitance of theparametric capacitance C(t) is varied. Also, the parametric reactancemay be created mechanically using wheels and the like. For a moredetailed discussion as to the various devices that may be used orapproaches taken to implement the parametric reactances 418, referenceis made to the following papers:

-   Manley, J. M. and Peterson, E., “Negative Resistance Effects in    Saturable Reactor Circuits,” AIEE Transactions, Vol. 65, December    1946, pp. 870-88;-   Mandelstam, L., Papalexi, N., Andronov, A., Chaikin, S., and Witt,    A., “Report on Recent Research on Nonlinear Oscillations,” Technical    Physics of the USSR, Leningrad, Volume 2, Number 2-3, pp 81-134,    1935;-   Mumford, W. W., “Some Notes on the History of Parametric    Transducers,” Proceedings of the IRE, Vol. 48, May 1960, pp.    848-853; and-   Raskin, J-P., Brown, A. R., Khuri-Yakub, B. T., Rebeiz, G. M., “A    Novel Parametric-Effect MEMS Amplifier,” Journal of    Microelectromechanical Systems, Vol. 9, December 2000, pp. 528-537.    Each of these references is incorporated herein by reference in    their entirety.

According to one embodiment, the power multipliers 400 a and 400 b areeach described as including a power multiplying network 403 a/403 bcomprising a multiply-connected, velocity inhibiting circuit constructedfrom a number of lumped-elements.

In addition, the term “lumped” is defined herein as effectivelyconcentrated at a single location. Thus, the terms “lumped-elements”refer to discrete, two-terminal, concentrated electrical elements suchas capacitance, inductances, resistance, and/or conductance. Thus, thelumped-elements as described herein may comprise discrete inductors,capacitors, or resistors. In addition, as contemplated herein,lumped-elements may also comprise diodes, transistors, and othersemi-conductors that may be described, for example, as nonlinearresistors or conductors that have resistance or conductance that iscontrolled by the polarity of applied voltages or currents, etc. Inaddition, lumped-elements may also comprise inherent capacitances,inductances, resistances, or conductances of various electricalstructures such as helices, parallel plates, or other structure as willbe discussed. Similar to the power multiplying network 203, thedirectional coupler 209 is also constructed using lumped-elements.

Lumped elements are circuit components for which the parametersinductance, capacitance, resistance, and conductance have the samemeaning as in the static situation. That is to say, the first orderterms in the electromagnetic power series solution of Maxwell'sequations are adequate to describe “lumped element” networks. Thisusually occurs when the dimensions of the components, includinginterconnections, is very small compared to the wavelength of operation.As the ratio of network dimension to wavelength is decreased, Maxwell'srigorous field equations transition to the distributed-elementtransmission line equations of Heaviside, and, in the limit, these passto the lumped element circuit equations of Kirchoff. Only the latter arenecessary to describe electrical circuits operating in the lumpedelement regiem of conventional electronic circuit theory. No spatialintegrals or spatial derivatives are necessary to analyze discretecomponent networks as would be required for distributed-elements andradiating circuits.

According to various embodiments, the parametric excitation as describedabove applies to power multipliers that comprise distributed elementcircuits as well. A distributed element circuit is a circuit whosereactance (inductance and/or capacitance) are distributed over aphysical distance that is comparable to an operating wavelength of thecircuit. Power multipliers that include a ring comprising a distributedelement circuit include those that substantially are not velocityinhibiting circuits. For distributed element power multipliers,Maxwell's rigorous field equations transition to the distributed-elementtransmission line equations of Heaviside. A distributed element powermultiplier are analyzed using spatial integrals or spatial derivatives.A distributed element power multiplier is one with a waveguidecomprising a ring with a physical circumference that is an integermultiple of the wavelength λ_(w) of an exciting traveling wave thataccumulates in the ring. It follows that for a distributed element powermultiplier to be practical, the frequency of operation is relativelyhigh, resulting a relatively small structure that can be practicallyconstructed. In this respect, the power multiplier 100 (FIG. 1)comprises a distributed element power multiplier.

In another embodiment, the principles of parametric excitation of apower multiplier described above with reference to the lumped-elementpower multipliers 400 a/400 b apply equally to distributed element powermultipliers. The reactance parameters of distributed ring powermultipliers may be varied in space and time (“pumped”) appropriately byany one of a variety of means. For example, the transmission lineelectrical parameters may be pumped by employing a magnetically biasedplasma. They may be pumped by using a magnetically biased permeabilityvarying in space and time, μ(x,t). Also, they may be pumpedappropriately by using a voltage-controlled electrical permittivity,∈(x,t), in the transmission line. Such techniques, obviously, have theeffect of pumping the inductance per unit length L(x,t) and thecapacitance per unit length C(x,t), respectively, at the desired pumpfrequency and phase. For one discussion of techniques for pumpingreactance variations in the context of conventional distributed elementparametric amplifiers, reference is made to Louisell, W. H., CoupledMode and Parametric Electronics, John Wiley and Sons, Inc., 1960, pp.131-147, and the references cited and discussed therein, which isincorporated herein by reference.

The power multipliers described (i.e. the power multipliers 400 a/400 b,and other embodiments such as distributed element power multipliers)above that employ the principles of parametric excitation may beemployed in the same manner as the power multipliers 200 and 250described above. For example, the power multipliers 400 a/400 b may beemployed for power smoothing with respect to power distribution networks300 as described above. Also, the power multipliers 400 a/400 b (ordistributed element power multipliers employing parametric excitation)may be employed in any other situation where the multiplication orstorage of power is desired, where the essential difference between thepower multipliers that employ parametric excitation and the powermultipliers that do not is that the power multipliers that employparametric excitation can buildup or store a vastly greater amount ofpower due to the fact that the physical resistance in the ringsassociated with such power multipliers is negated as described above.

It should be emphasized that the above-described embodiments of thepresent invention are merely possible examples of implementations,merely set forth for a clear understanding of the principles of theinvention. Many variations and modifications may be made to theabove-described embodiment(s) of the invention without departingsubstantially from the spirit and principles of the invention. All suchmodifications and variations are intended to be included herein withinthe scope of this disclosure and the present invention and protected bythe following claims.

1. A power multiplication apparatus, comprising: a ring power multiplierhaving a ring; and a parametric reactance that negates at least aportion of a physical resistance of the ring.
 2. The powermultiplication apparatus of claim 1, wherein the parametric reactance isvaried by approximately at least twice the frequency of a power signalapplied to the ring power multiplier.
 3. The power multiplicationapparatus of claim 1, wherein the parametric reactance further comprisesa parametric inductance.
 4. The power multiplication apparatus of claim3, wherein the parametric inductance is non-linear.
 5. The powermultiplication apparatus of claim 3, wherein the parametric inductancefurther comprises a magnetic amplifier.
 6. The power multiplicationapparatus of claim 1, wherein the parametric reactance further comprisesa parametric capacitance.
 7. The power multiplication apparatus of claim6, wherein parametric capacitance is non-linear.
 8. The powermultiplication apparatus of claim 6, wherein parametric capacitancefurther comprises a dielectric amplifier.
 9. The power multiplicationapparatus of claim 1, wherein the ring comprises a distributed element.10. The power multiplication apparatus of claim 9, wherein theparametric reactance further comprises a parametricreactance-per-unit-length.
 11. The power multiplication apparatus ofclaim 1, wherein the ring comprises a power multiplying network having amultiply-connected, velocity inhibiting circuit constructed from aplurality of lumped-elements.
 12. The power multiplication apparatus ofclaim 11, wherein the parametric reactance further comprises aparametric lumped-element reactance.
 13. The power multiplicationapparatus of claim 11, wherein the ring power multiplier furthercomprises: a launching network; and a directional coupler coupling thelaunching network to the power multiplying network.
 14. The powermultiplication apparatus of claim 11, further comprising a divertercoupled to the power multiplying network.
 15. A method for powermultiplication, comprising: coupling AC power into a ring of a ringpower multiplier; and negating at least a portion of a physicalresistance of the ring by driving a parametric reactance associated withthe ring.
 16. The method of claim 15, further comprising the step ofvarying the parametric reactance by approximately at least twice thefrequency of the AC power coupled into the ring of the ring powermultiplier.
 17. The method of claim 15, wherein the driving of theparametric reactance associated with the ring further comprises drivinga parametric inductance.
 18. The method of claim 17, wherein the drivingof the parametric inductance further comprises driving a non-linearparametric inductance.
 19. The method of claim 17, wherein the drivingof the parametric inductance further comprises driving a magneticamplifier.
 20. The method of claim 15, wherein the driving of theparametric reactance associated with the ring further comprises drivinga parametric capacitance.
 21. The method of claim 20, wherein thedriving of the parametric capacitance further comprises driving anon-linear parametric capacitance.
 22. The method of claim 20, whereinthe driving of the parametric capacitance further comprises driving adielectric amplifier.
 23. The method of claim 15, further comprising thestep of inhibiting a velocity of the AC power in the ring using adistributed element.
 24. The method of claim 23, wherein the driving ofthe parametric reactance associated with the ring further comprisesdriving a parametric reactance-per-unit-length.
 25. The method of claim15, further comprising the step of inhibiting a velocity of the AC powerin the ring using a power multiplying network having amultiply-connected circuit constructed from a plurality oflumped-elements.
 26. The method of claim 25, wherein the driving of theparametric reactance associated with the ring further comprises drivinga parametric lumped-element reactance.
 27. The method of claim 25,further comprising the steps of launching the AC power into a launchingnetwork; and coupling the AC power from the launching network into thepower multiplying network using a directional coupler.
 28. The method ofclaim 25, further comprising the step of diverting the AC power out ofthe ring to a load.
 29. A system for power multiplication, comprising:means for coupling AC power into a ring of a ring power multiplier; andmeans for negating at least a portion of a physical resistance of thering.
 30. The system of claim 29, wherein the means for negating thephysical resistance of the ring further comprises a parametricreactance.
 31. The system of claim 30, wherein the parametric reactanceis varied by at least twice the frequency of a power signal applied tothe ring power multiplier.
 32. The system of claim 30, wherein theparametric reactance further comprises a parametric inductance.
 33. Thesystem of claim 30, wherein the parametric reactance further comprises aparametric capacitance.
 34. The system of claim 30, wherein the ringcomprises a distributed element.
 35. The system of claim 30, wherein thering comprises a power multiplying network having a multiply-connected,velocity inhibiting circuit constructed from a plurality oflumped-elements.